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Math 6+ winter description

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Tim Welsh

Math 6+ winter description

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Print Learning Continuum ­ Test View Growth: Math 6+ CA 2010 Goal: Operations and Algebraic Thinking Sub­goal: Expressions and Equations 231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts Algebraic Expressions •  Translates between verbal and algebraic expressions •  Multiplies two binomial expressions •  Generates equivalent nonlinear expressions by combining like terms •  Generates equivalent linear expressions by combining like terms •  Evaluates linear expressions at given values with variables involving negative rational numbers •  Evaluates linear expressions at given values with variables involving positive rational numbers •  Evaluates nonlinear expressions at given values with variables involving positive rational numbers •  Writes algebraic expressions from a mathematical description of its component parts, including sum, product, quotient, term, and coefficient •  Adds and subtracts polynomials •  Interprets the coefficient and constant in a linear expression within the context of a real­world relationship •  Evaluates nonlinear expressions at given values with variables involving negative rational numbers •  Identifies the mathematical components of an algebraic expression, including sum, product, quotient, term, and coefficient •  Multiplies a polynomial by a monomial •  Writes linear expressions in one variable to represent real­world or mathematical contexts •  Generates equivalent linear expressions by using the associative, commutative, and distributive properties, and by combining like terms •  Generates equivalent linear expressions by using the associative, commutative, or distributive property •  Simplifies rational expressions •  Interprets the variable in a linear expression within the context of a real­world relationship •  Interprets equivalent linear expressions within a real­world context •  Multiplies two binomial expressions •  Generates equivalent nonlinear expressions by combining like terms •  Generates equivalent linear expressions by combining like terms •  Evaluates linear expressions at given values with variables involving negative rational numbers •  Evaluates nonlinear expressions at given values with variables involving positive rational numbers •  Multiples monomials •  Adds and subtracts polynomials •  Factors polynomials using a difference of squares •  Interprets the coefficient and constant in a linear expression within the context of a real­ world relationship •  Interprets the factors of a polynomial within the context of a real­world relationship •  Identifies the mathematical components of an algebraic expression, including sum, product, quotient, term, and coefficient •  Multiplies a polynomial by a monomial •  Factors quadratic trinomials •  Writes linear expressions in one variable to represent real­world or mathematical contexts •  Generates equivalent linear expressions by using the associative, commutative, and distributive properties, and by combining like terms •  Generates equivalent linear expressions by using the associative, commutative, or distributive property •  Factors polynomials with a degree greater than 2 by identifying common monomial factors and factoring the resulting polynomial •  Multiplies polynomials •  Simplifies rational expressions •  Interprets equivalent linear expressions within a real­world context •  Multiplies two binomial expressions •  Writes a rational expression as a sum of a polynomial and a proper rational expression •  Generates equivalent nonlinear expressions by using the associative, commutative, and distributive properties, and by combining like terms •  Multiples monomials •  Adds and subtracts polynomials •  Factors polynomials using a difference of squares •  Interprets the factors of a polynomial within the context of a real­world relationship •  Identifies the mathematical components of an algebraic expression, including sum, product, quotient, term, and coefficient •  Factors polynomials with a degree greater than 2 by identifying common monomial factors •  Multiplies a polynomial by a monomial •  Factors quadratic trinomials •  Writes linear expressions in one variable to represent real­world or mathematical contexts •  Interprets the constant in a quadratic expression within the context of a real­ world relationship •  Generates equivalent linear expressions by using the associative, commutative, and distributive properties, and by combining like terms Area
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Applies the distributive property of multiplication to find the area of rectangles with whole­number sides Decimals: Represent and Solve Word Problems •  Represents one­step word problems with expressions or equations and involving decimals with the same number of digits after the decimal point, including contexts involving money Exponents •  Uses substitution to determine an unknown exponent in an equation •  Represents a whole number as a power of a whole number •  Uses properties of exponents to simplify numerical expressions involving whole­ number exponents only •  Evaluates numbers with negative integer bases and whole­number exponents •  Uses substitution to determine an unknown exponent in an equation •  Uses properties of exponents to simplify numerical expressions involving negative integer exponents, including zero •  Uses properties of exponents to simplify numerical expressions involving whole­ number exponents only •  Uses substitution to determine an unknown exponent in an equation •  Uses properties of exponents to simplify numerical expressions involving negative integer exponents, including zero •  Uses properties of exponents to simplify numerical expressions involving whole­ number exponents only Fractions: Represent and Solve Word Problems •  Represents and solves word problems involving division of whole numbers where the quotient is a fraction •  Represents and solves word problems involving division of whole numbers where the quotient is a fraction •  Represents word problems involving multiplication of fractions or mixed numbers with expressions or equations Inequalities
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Writes and solves a one­step linear inequality in one variable involving a real­ world or mathematical context •  Solves one­step linear inequalities with negative rational numbers •  Solves two­step linear inequalities •  Writes a one­step linear inequality in one variable to represent a real­world or mathematical context •  Writes a quadratic inequality in one variable to represent a real­world or mathematical context •  Determines whether a linear equation or inequality is true for a given value of the variable •  Writes a multi­step linear inequality in one variable to represent a real­world or mathematical context •  Writes a compound inequality to represent a real­world or mathematical context •  Writes a two­step linear inequality in one variable to represent a real­world or mathematical context •  Writes an inequality in the form x > c or x < c to represent a real­world or mathematical context •  Represents an inequality in the form x>c or x<c on a number line given a real­world or mathematical context •  Writes and solves a one­step linear inequality in one variable involving a real­ world or mathematical context •  Solves one­step linear inequalities with negative rational numbers •  Solves two­step linear inequalities •  Writes a compound inequality to represent a set of real numbers shown on a number line •  Writes and solves a two­step linear inequality in one variable involving a real­ world or mathematical context •  Represents the solutions of a two­step linear inequality on a number line •  Solves multi­step linear inequalities •  Represents the solutions of a one­step linear inequality on a number line •  Writes a one­step linear inequality in one variable to represent a real­world or mathematical context •  Determines whether a linear equation or inequality is true for a given value of the variable •  Writes an inequality in the form x>c or x<c to represent a set of real numbers shown on a number line •  Writes a multi­step linear inequality in one variable to represent a real­world or mathematical context •  Represents the solutions of a compound linear inequality on a number line •  Writes a compound inequality to represent a real­world or mathematical context •  Writes a multi­step rational inequality in one variable to represent a real­world or mathematical context •  Writes a two­step linear inequality in one variable to represent a real­world or mathematical context •  Writes an inequality in the form x > c or x < c to represent a real­world or mathematical context •  Solves compound linear inequalities •  Solves one­step linear inequalities with negative rational numbers •  Solves two­step linear inequalities •  Represents the solutions of a multistep linear inequality on a number line •  Represents the solutions of a two­ variable linear inequality on the coordinate plane •  Writes a linear inequality to represent a region on the coordinate plane •  Writes a compound inequality to represent a set of real numbers shown on a number line •  Represents the solutions of a two­step linear inequality on a number line •  Solves multi­step linear inequalities •  Represents a compound inequality on a number line given a real­world or mathematical context •  Writes a compound inequality to represent a real­world or mathematical context Linear Functions
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Understands independent and dependent variables within a linear context •  Graphs a linear function of the form y = mx given a simple scenario •  Writes an equation in the form y = mx to represent the relationship between real­ world quantities given a table of values or two ordered pairs •  Compares the rate of change between two proportional relationships represented in different ways •  Writes an equation in the form y = mx to represent the relationship between real­ world quantities given a graph •  Understands that the slope is the same between any two points on a line •  Writes the equation of a line in the form y = mx given a table of values or two ordered pairs •  Writes an equation in the form y = mx to represent the relationship between real­ world quantities given a simple scenario •  Understands independent and dependent variables within a linear context •  Writes an equation in the form y = mx to represent the relationship between real­ world quantities given a table of values or two ordered pairs •  Writes the equation of a line in the form y = mx given a graph •  Compares the rate of change between two proportional relationships represented in different ways •  Understands that the slope is the same between any two points on a line •  Graphs the equation of a line in the form y = mx •  Writes the equation of a line in the form y = mx given a table of values or two ordered pairs •  Understands independent and dependent variables within a linear context •  Understands that the slope is the same between any two points on a line •  Writes the equation of a line in standard form given a table of values or two ordered pairs •  Represents a proportional relationship in more than one form, including tables, graphs, equations, and verbal descriptions Number Sentences/Equations/Equivalence
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Solves two­step linear equations with positive rational numbers •  Solves multi­step linear equations with positive and negative rational numbers •  Determines the number of solutions of a linear equation in one variable given the corresponding equation in the form x=a, x=x, or a=b •  Writes a multi­step linear equation in one variable to represent a real­world or mathematical context •  Evaluates formulas or linear equations at given values for the variables •  Writes a two­step linear equation in one variable to represent a real­world or mathematical context •  Identifies an ordered pair that is a solution to a two­variable equation •  Solves one­step linear equations with negative rational numbers •  Solves quadratic equations in the form x² = c •  Determines whether a linear equation or inequality is true for a given value of the variable •  Solves one­step linear equations with positive rational numbers •  Writes and solves a multi­step quadratic equation in one variable involving a real­ world or mathematical context •  Solves quadratic equations in one variable using factoring, the quadratic formula, or other appropriate method •  Writes the equation of a vertical line given a graph •  Solves two­step linear equations with negative rational numbers •  Writes and solves a one­step quadratic equation in the form x² = c involving a real­ world or mathematical context •  Solves cubic equations by taking cube roots •  Writes and solves a two­step linear equation in one variable involving a real­ world or mathematical context •  Solves radical equations that lead to linear equations •  Writes a quadratic equation in one variable to represent a real­world or mathematical context •  Solves two­step linear equations with positive rational numbers •  Solves multi­step linear equations with positive and negative rational numbers •  Applies the simple interest formula to solve for the interest rate, principal, or time invested •  Writes a multi­step linear equation in one variable to represent a real­world or mathematical context •  Evaluates formulas or linear equations at given values for the variables •  Writes and solves a multi­step linear equation in one variable involving a real­ world or mathematical context •  Solves radical equations that lead to a quadratic equation •  Identifies an ordered pair that is a solution to a two­variable equation •  Solves quadratic equations in the form x² = c •  Determines whether a linear equation or inequality is true for a given value of the variable •  Determines the number of solutions of a linear equation in one variable by transforming the equation into an equivalent one to reach a decision •  Writes and solves a multi­step quadratic equation in one variable involving a real­ world or mathematical context •  Solves quadratic equations in one variable using factoring, the quadratic formula, or other appropriate method •  Solves rational equations •  Solves literal equations for linear variables •  Solves two­step linear equations with negative rational numbers •  Writes and solves a one­step quadratic equation in the form x² = c involving a real­ world or mathematical context •  Writes and solves a two­step linear equation in one variable involving a real­ world or mathematical context •  Solves radical equations that lead to linear equations •  Writes a quadratic equation in one variable to represent a real­world or mathematical context •  Solves multi­step linear equations with positive and negative rational numbers •  Writes a multi­step linear equation in one variable to represent a real­world or mathematical context •  Writes and solves a multi­step linear equation in one variable involving a real­ world or mathematical context •  Solves radical equations that lead to a quadratic equation •  Solves literal equations for nonlinear variables •  Identifies an ordered pair that is a solution to a two­variable equation •  Solves quadratic equations with complex solutions •  Understands the relationship between the points of intersection of the graphs of f(x) and g(x) and the solutions to the equation f(x) = g(x) •  Determines the number of solutions of a linear equation in one variable by transforming the equation into an equivalent one to reach a decision •  Writes and solves a multi­step quadratic equation in one variable involving a real­ world or mathematical context •  Solves quadratic equations in one variable using factoring, the quadratic formula, or other appropriate method •  Solves rational equations •  Solves literal equations for linear variables •  Writes and solves a one­step quadratic equation in the form x² = c involving a real­ world or mathematical context •  Solves radical equations that lead to linear equations Numerical Expressions
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Evaluates numerical expressions involving multiple operations with whole numbers, no parenthesis •  Applies the order of operations, with grouping symbols and with whole­number exponents, to simplify numerical expressions consisting of positive rational numbers •  Applies the order of operations, with grouping symbols and whole­number exponents, to simplify numerical expressions involving both positive and negative rational numbers •  Applies the order of operations, without grouping symbols or whole­number exponents, to simplify numerical expressions involving positive rational numbers •  Uses properties of exponents to simplify numerical expressions involving whole­ number exponents only •  Applies the order of operations, with grouping symbols and excluding exponents, to simplify numerical expressions involving both positive and negative rational numbers •  Applies the order of operations, without grouping symbols or whole­number exponents, to simplify numerical expressions involving both positive and negative rational numbers •  Evaluates numerical expressions involving multiple operations with whole numbers and parentheses •  Applies the order of operations, without grouping symbols and with whole­number exponents, to simplify numerical expressions consisting of positive rational numbers •  Applies the order of operations, with grouping symbols and with whole­number exponents, to simplify numerical expressions consisting of positive rational numbers •  Uses properties of exponents to simplify numerical expressions involving negative integer exponents, including zero •  Applies the order of operations, with grouping symbols and whole­number exponents, to simplify numerical expressions involving both positive and negative rational numbers •  Uses properties of exponents to simplify numerical expressions involving whole­ number exponents only •  Applies the order of operations, without grouping symbols or whole­number exponents, to simplify numerical expressions involving both positive and negative rational numbers •  Applies the order of operations, with whole­number exponents and excluding grouping symbols, to simplify numerical expressions involving both positive and negative rational numbers •  Uses properties of exponents to simplify numerical expressions involving negative integer exponents, including zero •  Applies the order of operations, with grouping symbols and whole­number exponents, to simplify numerical expressions involving both positive and negative rational numbers •  Uses properties of exponents to simplify numerical expressions involving whole­ number exponents only Patterns/Sequences/Series •  Determines missing values in a function table representing a nonproportional relationship, rule not given Polynomial Functions •  Identifies the zeros of a polynomial function from a graph •  Identifies the zeros of a polynomial function from a graph •  Identifies the zeros of a polynomial function from a graph Properties and Relationships of Operations
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Applies the distributive property of multiplication to whole numbers •  Applies the distributive property of multiplication to find the area of rectangles with whole­number sides Quadratic Functions •  Writes a quadratic function given the zeros Radicals •  Evaluates the square root of a perfect square Rate of Change/Slope •  Compares the rate of change between two proportional relationships represented in different ways •  Understands that the slope is the same between any two points on a line •  Compares the rate of change between two proportional relationships represented in different ways •  Understands that the slope is the same between any two points on a line •  Understands that the slope is the same between any two points on a line Rational Numbers: Solve Real­World and Mathematical Problems •  Solves real­world problems using appropriate problem­solving strategies and evaluates the reasonableness of the solutions •  Solves real­world problems using appropriate problem­solving strategies and evaluates the reasonableness of the solutions •  Solves real­world problems using appropriate problem­solving strategies and evaluates the reasonableness of the solutions Scientific Notation •  Determines the relative magnitude of two numbers expressed in scientific notation •  Solves real­world problems with numbers expressed in scientific notation •  Converts a number from standard form to scientific notation •  Multiplies and divides numbers expressed in scientific notation •  Determines the relative magnitude of two numbers expressed in scientific notation •  Solves real­world problems with numbers expressed in scientific notation •  Converts a number from standard form to scientific notation •  Multiplies and divides numbers expressed in scientific notation •  Approximates very large and very small quantities using scientific notation •  Determines the relative magnitude of two numbers expressed in scientific notation •  Multiplies and divides numbers expressed in scientific notation System of Equations/Inequalities
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Writes a system of linear inequalities to represent a real­world or mathematical context •  Solves a system of linear equations graphically •  Writes a system of linear equations to represent a real­world or mathematical context •  Identifies an ordered pair that is a solution to a system of linear inequalities •  Writes and solves a system of linear equations involving a real­world or mathematical context •  Solves a system of linear equations algebraically •  Solves a system of equations with one linear and one quadratic equation algebraically •  Writes a system of linear inequalities to represent a real­world or mathematical context •  Shows the steps to solve a system of linear equations using linear combinations •  Writes a system of linear equations to represent a real­world or mathematical context •  Identifies an ordered pair that is a solution to a system of linear inequalities •  Writes and solves a system of linear equations involving a real­world or mathematical context •  Solves a system of linear equations algebraically •  Solves a system of equations with one linear and one quadratic equation algebraically •  Writes a system of linear inequalities to represent a real­world or mathematical context •  Writes a system of linear equations given a graph •  Shows the steps to solve a system of linear equations using linear combinations •  Solves a system of linear equations given a table •  Graphs a system of linear inequalities •  Writes a system of linear equations to represent a real­world or mathematical context •  Identifies an ordered pair that is a solution to a system of linear inequalities •  Writes and solves a system of linear equations involving a real­world or mathematical context •  Graphs a system of linear equations •  Solves a system of linear equations algebraically •  Shows the steps to solve a system of linear equations using the substitution method Whole Numbers: Represent and Solve Word Problems •  Represents and solves word problems involving division of whole numbers where the quotient is a fraction •  Represents multi­step word problems involving the four operations with expressions or equations, whole numbers •  Represents and solves word problems involving division of whole numbers where the quotient is a fraction •  Represents multi­step word problems involving the four operations with expressions or equations, whole numbers Sub­goal: Use Functions to Model Relationships 231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts Exponential and Logarithmic Functions
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Identifies the appropriate linear or exponential model that represents a real­ world situation •  Evaluates an exponential function for a given value in its domain to solve a real­ world problem •  Compares the growth of a linear function to the growth of an exponential function in terms of a context •  Compares the growth of a quadratic function to the growth of an exponential function in terms of a context •  Understands that exponential models grow and decay by equal factors over equal intervals •  Classifies exponential functions as representations of growth or decay •  Identifies the appropriate linear or exponential model that represents a real­ world situation •  Evaluates an exponential function for a given value in its domain to solve a real­ world problem •  Describes the effects of changes in parameters on exponential functions that represent real­world relationships •  Understands that exponential models grow and decay by equal factors over equal intervals •  Writes exponential functions to represent real­world or mathematical problems •  Classifies exponential functions as representations of growth or decay •  Describes the effects that changes in parameters have on the graphs of exponential functions •  Identifies the appropriate linear or exponential model that represents a real­ world situation •  Describes the effects of changes in parameters on exponential functions that represent real­world relationships •  Understands that exponential models grow and decay by equal factors over equal intervals •  Writes exponential functions to represent real­world or mathematical problems •  Determines real­world situations that can be modeled by an exponential function •  Graphs exponential functions •  Writes an exponential function given a table of values Linear Functions •  Writes an equation in the form y = mx + b to represent the relationship between real­ world quantities given a simple scenario •  Interprets the meaning of the constant term in the equation y = mx + b within the context of a real­world linear relationship •  Compares the growth of a linear function to the growth of an exponential function in terms of a context •  Calculates the rate of change from a table or description of a real­world linear relationship •  Graphs a linear function of the form y = mx + b given a table of values •  Compares the rate of change and intercepts between two nonproportional linear functions represented in different ways •  Translates between the graph of a linear function and a verbal description of the real­world relationship •  Writes an equation in the form y = mx + b to represent the relationship between real­ world quantities given a complex scenario •  Interprets the meaning of the slope and y­intercept of a graph within the context of a real­world linear relationship •  Writes an equation in the form y = mx + b to represent the relationship between real­ world quantities given a table of values or two ordered pairs •  Understands a function is linear if it can be represented algebraically by an equation in the form y = mx + b •  Interprets the meaning of the constant term in the equation y = mx + b within the context of a real­world linear relationship •  Calculates the rate of change from a table or description of a real­world linear relationship •  Calculates the slope of a line on a graph •  Illustrates the result of changes in the slope and y­intercept within a real­world linear relationship •  Compares the rate of change and intercepts between two nonproportional linear functions represented in different ways •  Writes an equation in the form y = mx + b to represent the relationship between real­ world quantities given a complex scenario •  Understands that linear functions increase and decrease by equal differences over equal intervals •  Graphs the equation of a line in the form y = mx + b •  Calculates the slope of a line given ordered pairs •  Writes an equation in the form y = mx + b to represent the relationship between real­ world quantities given a table of values or two ordered pairs •  Graphs the equation of a line given the slope and a point on the line •  Understands a function is linear if it can be represented algebraically by an equation in the form y = mx + b •  Interprets the meaning of the slope for the equation y = mx + b within the context of a •  Illustrates the result of changes in the slope and y­intercept within a real­world linear relationship •  Compares the rate of change and intercepts between two nonproportional linear functions represented in different ways •  Interprets the meaning of the initial value in a table within the context of a real­world linear relationship •  Writes an equation in the form y = mx + b to represent the relationship between real­ world quantities given a complex scenario •  Understands that linear functions increase and decrease by equal differences over equal intervals •  Graphs the equation of a line in the form y = mx + b •  Writes the equation of a line in the form y = mx + b given the slope and a point on the line •  Calculates the slope of a line given ordered pairs •  Writes an equation in the form y = mx + b to represent the relationship between real­ world quantities given the slope and y­ intercept •  Compares two linear functions represented in different ways to solve problems •  Interprets the meaning of the y­intercept of a graph within the context of a real­world linear relationship
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Writes an equation in the form y = mx + b to represent the relationship between real­ world quantities given the slope and y­ intercept •  Compares two linear functions represented in different ways to solve problems •  Interprets the meaning of the y­intercept of a graph within the context of a real­world linear relationship •  Writes the equation of a line in the form y = mx + b given a graph •  Calculates the rate of change from a graph representing a real­world linear relationship •  Identifies an intercept of a graph of a linear function •  Interprets the meaning of the y­intercept for the equation y = mx + b within the context of a real­world linear relationship •  Identifies the table of values given a graph of a linear relationship in the form y = mx + b •  Translates between the graph of a piecewise linear function and a verbal description of the real­world relationship •  Writes the equation representing transformations of linear functions, including the transformations y = af(x), y = f(ax), y = f(x − a), and y = f(x) + a •  Describes a situation that can be represented by a given linear equation •  Calculates the initial value from a table or description of a real­world linear relationship •  Writes the equation of a line in the form y = mx + b given a table of values or two ordered pairs •  Interprets the meaning of the slope of a graph in a real­world linear relationship •  Describes the effects of changes in parameters on linear functions that represent real­world relationships real­world linear relationship •  Writes an equation in the form y = mx + b to represent the relationship between real­ world quantities given the slope and y­ intercept •  Compares two linear functions represented in different ways to solve problems •  Interprets the meaning of the y­intercept of a graph within the context of a real­world linear relationship •  Determines the y­intercept of a line given two points on the line •  Writes the equation of a line in the form y = mx + b given a graph •  Translates between the graph of a piecewise linear function and a verbal description of the real­world relationship •  Describes the effects that changes in the constant terms have on the graphs of linear functions •  Calculates the initial value from a table or description of a real­world linear relationship •  Compares the rate of change and intercepts between two nonproportional linear functions represented in the same way •  Writes the equation of a line in the form y = mx + b given a table of values or two ordered pairs •  Interprets the meaning of the slope of a graph in a real­world linear relationship •  Writes the equation of a line in the form y = mx + b given a graph •  Graphs the equation of a line in standard form •  Describes the effects that changes in the constant terms have on the graphs of linear functions •  Calculates the initial value from a table or description of a real­world linear relationship •  Writes the equation of a line in the form y = mx + b given a table of values or two ordered pairs •  Interprets the meaning of the slope of a graph in a real­world linear relationship Patterns/Sequences/Series
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Determines the value of a term in a geometric sequence defined by a list •  Determines the value of a term in an arithmetic sequence given a contextual situation •  Determines the value of a term in a geometric sequence given a contextual situation •  Writes an expression or formula for the nth term of an arithmetic sequence given a contextual situation •  Determines the value of a term in a geometric sequence defined by a list •  Determines the value of a term in an arithmetic sequence given a contextual situation •  Writes an expression or formula for the nth term of an arithmetic sequence given a number sequence •  Determines the value of a term in a geometric sequence given a contextual situation •  Writes an expression or formula for the nth term of an arithmetic sequence given a contextual situation •  Determines the value of a term in a geometric sequence defined by a list •  Determines the value of a term in an arithmetic sequence given a contextual situation •  Writes an expression or formula for the nth term of an arithmetic sequence given a number sequence •  Determines the value of a term in a geometric sequence given a contextual situation •  Writes an expression or formula for the nth term of a geometric sequence given a number sequence •  Writes an expression or formula for the nth term of an arithmetic sequence given a contextual situation Piecewise/Absolute Value Functions •  Translates between the graph of a piecewise linear function and a verbal description of the real­world relationship •  Calculates the rate of change of a piecewise function over a given interval •  Graphs absolute value functions •  Describes the effects of transformations on the graphs of absolute value functions, including the transformations y = af(x), y = f(ax), y = f(x − a), and y = f(x) + a •  Translates between the graph of a piecewise linear function and a verbal description of the real­world relationship •  Calculates the rate of change of a piecewise function over a given interval •  Graphs absolute value functions •  Calculates the rate of change of a piecewise function over a given interval Properties and Operations of Functions •  Determines the input of a function given an output •  Understands a function is linear if it can be represented algebraically by an equation in the form y = mx + b •  Performs operations with functions •  Determines the range of a polynomial function •  Understands a function is linear if it can be represented algebraically by an equation in the form y = mx + b •  Determines the range of an absolute value function •  Performs operations with functions •  Distinguishes between linear and nonlinear functions given an equation, a graph, or a table of values •  Writes a function in the form f(x) = g(x) – h(x) to represent real­world scenarios •  Determines the range of an absolute value function •  Performs operations with functions •  Determines the range of a quadratic function •  Distinguishes between linear and nonlinear functions given an equation, a graph, or a table of values •  Determines the reasonable range of a function in a given situation Quadratic Functions
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Writes a quadratic function given a table of values •  Evaluates a quadratic function for a given value in its domain to solve a real­world problem •  Describes the effects that changes in the constant terms have on the graphs of quadratic functions •  Compares the growth of a quadratic function to the growth of an exponential function in terms of a context •  Identifies the vertex, intercepts, or axis of symmetry of a quadratic function given a graph •  Evaluates a quadratic function for a given value in its domain •  Graphs transformations of quadratic functions, including the transformations y = af(x), y = f(ax), y = f(x − a), and y = f(x) + a •  Identifies the table of values given a graph of a quadratic relationship •  Writes a quadratic function given a table of values •  Determines the zeros of a quadratic function from a table of values •  Evaluates a quadratic function for a given value in its domain to solve a real­world problem •  Calculates the average rate of change from a table or description of a real­world quadratic relationship •  Determines the maximum, minimum, y­ intercept, or zeros of a quadratic function to solve real­world problems •  Describes the effects that changes in the constant terms have on the graphs of quadratic functions •  Identifies the vertex, intercepts, or axis of symmetry of a quadratic function given a graph •  Graphs quadratic functions •  Evaluates a quadratic function for a given value in its domain •  Graphs transformations of quadratic functions, including the transformations y = af(x), y = f(ax), y = f(x − a), and y = f(x) + a •  Writes a quadratic function given a table of values •  Determines the zeros of a quadratic function from a table of values •  Evaluates a quadratic function for a given value in its domain to solve a real­world problem •  Determines the maximum, minimum, y­ intercept, or zeros of a quadratic function to solve real­world problems •  Writes a quadratic function to represent real­world or mathematical contexts •  Identifies the vertex, intercepts, or axis of symmetry of a quadratic function given a graph •  Graphs quadratic functions •  Evaluates a quadratic function for a given value in its domain Rate of Change/Slope •  Calculates the rate of change of a piecewise function over a given interval •  Interprets the meaning of the slope and y­intercept of a graph within the context of a real­world linear relationship •  Calculates the rate of change from a graph representing a real­world linear relationship •  Interprets the meaning of the slope of a graph in a real­world linear relationship •  Calculates the rate of change from a table or description of a real­world linear relationship •  Compares the rate of change and intercepts between two nonproportional linear functions represented in different ways •  Calculates the rate of change of a piecewise function over a given interval •  Calculates the average rate of change from a table or description of a real­world quadratic relationship •  Interprets the meaning of the slope for the equation y = mx + b within the context of a real­world linear relationship •  Interprets the meaning of the slope of a graph in a real­world linear relationship •  Calculates the slope of a line on a graph •  Compares the rate of change and intercepts between two nonproportional linear functions represented in the same way •  Calculates the rate of change from a table or description of a real­world linear relationship •  Calculates the slope of a line given ordered pairs •  Compares the rate of change and intercepts between two nonproportional linear functions represented in different ways •  Calculates the rate of change of a piecewise function over a given interval •  Interprets the meaning of the slope of a graph in a real­world linear relationship •  Calculates the slope of a line given ordered pairs •  Compares the rate of change and intercepts between two nonproportional linear functions represented in different ways Rational Functions
Goal: The Real and Complex Number Systems 231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Writes rational functions to represent real­world or mathematical problems •  Determines end behavior of rational functions Trigonometric Functions/Radian Measure •  Converts between radians and degrees •  Converts between radians and degrees •  Understands the relationship between radian measure and the length of an arc on the unit circle Sub­goal: Ratios and Proportional Relationships 231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts Capacity •  Completes complex conversions of customary units of capacity involving fractions, decimals, or more than two units •  Solves multi­step capacity word problems involving decimals or fractions and conversion of metric units •  Completes conversions of metric units of capacity •  Solves multi­step capacity word problems involving decimals or fractions and conversion of metric units •  Completes conversions of metric units of capacity •  Completes conversions of metric units of capacity Conversion of Units
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Completes conversions of metric units of mass •  Completes conversions of metric units of capacity •  Completes complex conversions of customary units of weight involving fractions, decimals, or more than two units •  Solves multi­step weight word problems involving whole numbers and conversion of customary units •  Converts units of length between the customary and the metric systems •  Solves multi­step length word problems involving whole numbers and conversion of customary units •  Converts unit rates to solve real­world problems •  Solves multi­step length word problems involving decimals or fractions and conversion of customary units •  Solves multi­step capacity word problems involving decimals or fractions and conversion of metric units •  Completes simple conversions of customary units of weight •  Completes conversions of metric units of length •  Completes complex conversions of customary units of capacity involving fractions, decimals, or more than two units •  Completes complex conversions of customary units of length involving fractions, decimals, or more than two units •  Converts units of speed •  Completes conversions of metric units of capacity •  Converts units of length between the customary and the metric systems •  Solves multi­step length word problems involving whole numbers and conversion of customary units •  Converts unit rates to solve real­world problems •  Solves multi­step length word problems involving decimals or fractions and conversion of customary units •  Solves multi­step capacity word problems involving decimals or fractions and conversion of metric units •  Completes conversions of metric units of length •  Solves real­world or mathematical area problems involving conversion of linear measurement •  Solves multi­step mass word problems involving whole numbers and conversion of metric units •  Completes complex conversions of customary units of length involving fractions, decimals, or more than two units •  Converts units of speed •  Completes conversions of metric units of capacity •  Converts unit rates to solve real­world problems •  Completes conversions of metric units of length •  Converts units of speed Length •  Completes conversions of metric units of length •  Solves multi­step length word problems involving whole numbers and conversion of customary units •  Converts units of length between the customary and the metric systems •  Completes complex conversions of customary units of length involving fractions, decimals, or more than two units •  Solves multi­step length word problems involving decimals or fractions and conversion of customary units •  Completes conversions of metric units of length •  Solves multi­step length word problems involving whole numbers and conversion of customary units •  Converts units of length between the customary and the metric systems •  Completes complex conversions of customary units of length involving fractions, decimals, or more than two units •  Solves multi­step length word problems involving decimals or fractions and conversion of customary units •  Completes conversions of metric units of length Problem Solving with Units
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Solves multi­step length word problems involving decimals or fractions and conversion of customary units •  Solves multi­step weight word problems involving whole numbers and conversion of customary units •  Solves multi­step capacity word problems involving decimals or fractions and conversion of metric units •  Solves multi­step length word problems involving whole numbers and conversion of customary units •  Solves multi­step length word problems involving decimals or fractions and conversion of customary units •  Solves multi­step mass word problems involving whole numbers and conversion of metric units •  Solves multi­step capacity word problems involving decimals or fractions and conversion of metric units •  Solves multi­step length word problems involving whole numbers and conversion of customary units Rates/Ratios/Proportions/Percents
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Writes a proportion to solve a real­world problem •  Calculates the percent one number is of another number for percents greater than 100% •  Uses two given unit rates to solve a multi­step real­world problem •  Solves one­step percent problems within a real­world or mathematical context •  Uses ratios of whole numbers and decimals to calculate unit rates •  Uses a given unit rate to solve a multi­ step real­world problem •  Uses tables to represent real­world relationships described by a given ratio •  Converts unit rates to solve real­world problems •  Solves real­world problems involving percent or fractional increase •  Converts between decimals and percents less than 100% •  Solves real­world and mathematical problems using ratios or proportional reasoning •  Converts between percents and ratios expressed verbally or in the form a:b •  Uses ratios of decimals to calculate unit rates •  Determines the whole in a real­world percent problem given the part and the percent •  Identifies the part­to­part ratio between two quantities •  Uses ratios of whole numbers to calculate unit rates •  Identifies the part­to­whole ratio between two quantities •  Determines equivalent ratios •  Compares unit rates within a real­world context •  Calculates percents of numbers •  Calculates the percent one number is of another number •  Calculates the whole when given a part and the percent •  Uses a given unit rate to solve a one­ step real­world problem •  Uses ratios of fractions to calculate unit rates •  Solves for a missing value in a proportion by taking a cross product •  Solves multi­step percent problems within a real­world or mathematical context •  Writes a proportion to solve a real­world problem •  Calculates the percent one number is of another number for percents greater than 100% •  Uses two given unit rates to solve a multi­ step real­world problem •  Solves one­step percent problems within a real­world or mathematical context •  Uses a given unit rate to solve a multi­step real­world problem •  Uses tables to represent real­world relationships described by a given ratio •  Converts unit rates to solve real­world problems •  Solves real­world problems involving percent or fractional increase •  Calculates simple interest •  Solves real­world and mathematical problems using ratios or proportional reasoning •  Converts between part­to­part ratios and part­to­whole ratios •  Identifies the part­to­whole ratio between two quantities •  Determines equivalent ratios •  Compares unit rates within a real­world context •  Calculates percents of numbers •  Calculates the percent one number is of another number •  Uses a given unit rate to solve a one­step real­world problem •  Uses ratios of fractions to calculate unit rates •  Solves for a missing value in a proportion by taking a cross product •  Solves multi­step percent problems within a real­world or mathematical context •  Writes a proportion to solve a real­world problem •  Calculates the percent one number is of another number for percents greater than 100% •  Uses two given unit rates to solve a multi­step real­world problem •  Uses a given unit rate to solve a multi­ step real­world problem •  Converts unit rates to solve real­world problems •  Solves real­world problems involving percent or fractional increase •  Calculates simple interest •  Solves real­world and mathematical problems using ratios or proportional reasoning •  Compares ratios within a real­world context •  Uses ratios of fractions to calculate unit rates •  Solves for a missing value in a proportion by taking a cross product •  Solves multi­step percent problems within a real­world or mathematical context Rational Numbers: Equivalence
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Converts between decimals and percents less than 100% •  Converts between percents and ratios expressed verbally or in the form a:b Rational Numbers: Solve Real­World and Mathematical Problems •  Determines the whole in a real­world percent problem given the part and the percent •  Solves multi­step percent problems within a real­world or mathematical context •  Solves one­step percent problems within a real­world or mathematical context •  Solves real­world problems involving percent or fractional increase •  Solves multi­step percent problems within a real­world or mathematical context •  Solves one­step percent problems within a real­world or mathematical context •  Solves real­world problems involving percent or fractional increase •  Calculates simple interest •  Solves multi­step percent problems within a real­world or mathematical context •  Solves real­world problems involving percent or fractional increase •  Calculates simple interest Weight/Mass •  Completes simple conversions of customary units of weight •  Solves multi­step weight word problems involving whole numbers and conversion of customary units •  Completes complex conversions of customary units of weight involving fractions, decimals, or more than two units •  Completes conversions of metric units of mass •  Solves multi­step mass word problems involving whole numbers and conversion of metric units Sub­goal: Perform Operations 231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts Absolute Value: Concepts/Properties •  Understands that the distance between two integers on a number line is equal to the absolute value of the difference Conversion of Units •  Applies dimensional analysis to manipulate units in a real­world problem •  Applies dimensional analysis to manipulate units in a real­world problem Decimals: Multiplication/Division
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Multiplies decimals by multi­digit whole numbers •  Multiplies decimals by decimals •  Divides decimals by whole numbers •  Divides decimals by decimals •  Multiplies or divides decimals by 10, 100, or 1,000 •  Divides whole numbers by decimals •  Divides decimals by decimals Decimals: Represent and Solve Word Problems •  Solves multi­step word problems involving the four operations and decimals, including contexts involving money •  Solves one­step word problems involving addition and subtraction of decimals with a different number of digits after the decimal point •  Solves one­step word problems involving multiplication of multi­digit whole numbers and decimals to the hundredths, including contexts involving money •  Solves one­step word problems involving multiplication of multi­digit whole numbers and decimals to the hundredths, including contexts involving money Fractions: Addition/Subtraction •  Adds and subtracts whole numbers, fractions, and/or mixed numbers with unlike denominators, with regrouping •  Adds and subtracts fractions with denominators of 10 or 100 •  Adds and subtracts whole numbers, fractions, and/or mixed numbers with unlike denominators, no regrouping •  Adds and subtracts whole numbers, fractions, and/or mixed numbers with like denominators, with regrouping •  Adds and subtracts fractions with unlike denominators •  Adds and subtracts whole numbers, fractions, and/or mixed numbers with unlike denominators, with regrouping Fractions: Multiple Operations •  Simplifies complex fractions Fractions: Multiplication/Division
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Divides mixed numbers by fractions, results in simplest form •  Multiplies mixed numbers by mixed numbers, results in simplest form •  Multiplies fractions by fractions, results in simplest form •  Divides mixed numbers by mixed numbers, results in simplest form •  Divides whole numbers by fractions using models •  Understands the effect of multiplying whole numbers by fractions greater than 1  •  Divides fractions by whole numbers, results in simplest form •  Understands the effect of multiplying whole numbers by fractions less than 1 •  Divides fractions by fractions, results in simplest form •  Multiplies mixed numbers by whole numbers, results in simplest form •  Divides whole numbers by fractions, results in simplest form •  Understands that dividing by a fraction is the same as multiplying by its reciprocal •  Understands that multiplying whole numbers and fractions involves multiplying the whole number and the numerator, then dividing by the denominator •  Divides mixed numbers by fractions using models •  Divides whole numbers by mixed numbers, results in simplest form •  Multiplies mixed numbers by fractions, results in simplest form •  Divides fractions by mixed numbers, results in simplest form •  Divides mixed numbers by whole numbers, results in simplest form •  Divides mixed numbers by fractions, results in simplest form •  Multiplies mixed numbers by mixed numbers, results in simplest form •  Divides mixed numbers by mixed numbers, results in simplest form •  Divides fractions by fractions, results in simplest form •  Divides whole numbers by fractions, results in simplest form •  Understands that multiplying whole numbers and fractions involves multiplying the whole number and the numerator, then dividing by the denominator •  Divides mixed numbers by fractions using models •  Multiplies mixed numbers by fractions, results in simplest form •  Divides mixed numbers by whole numbers, results in simplest form Fractions: Represent and Solve Word Problems
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Solves one­step word problems involving division of fractions or mixed numbers by whole numbers •  Solves one­step word problems involving division of fractions or mixed numbers •  Solves one­step word problems involving addition and subtraction of mixed numbers with unlike denominators •  Solves multi­step word problems involving whole numbers, fractions and/or mixed numbers •  Solves one­step word problems involving multiplication of fractions or mixed numbers •  Solves one­step word problems involving division of unit fractions by whole numbers •  Solves multi­step word problems involving addition and subtraction of fractions with unlike denominators •  Solves one­step word problems involving addition and subtraction of mixed numbers with like denominators •  Solves one­step word problems involving division of whole numbers by unit fractions •  Solves one­step word problems involving addition and subtraction of fractions with unlike denominators •  Solves one­step word problems involving multiplication of whole numbers and either fractions or mixed numbers •  Solves one­step word problems involving division of fractions or mixed numbers by whole numbers •  Solves one­step word problems involving division of fractions or mixed numbers •  Solves one­step word problems involving multiplication of fractions or mixed numbers •  Solves one­step word problems involving multiplication of whole numbers and either fractions or mixed numbers •  Solves one­step word problems involving division of fractions or mixed numbers •  Solves one­step word problems involving multiplication of fractions or mixed numbers Integers: Computation •  Represents addition and subtraction of integers on a number line •  Understands subtracting an integer is the same as adding its opposite Numerical Expressions •  Represents real­world problems involving the addition and subtraction of integers with numerical expressions •  Rewrites the sum of two whole numbers as a product of a common factor and the sum of two whole numbers •  Rewrites the sum of two whole numbers as a product of a common factor and the sum of two whole numbers •  Rewrites the sum of two whole numbers as a product of a common factor and the sum of two whole numbers Problem Solving with Units •  Applies dimensional analysis to manipulate units in a real­world problem •  Applies dimensional analysis to manipulate units in a real­world problem Properties and Relationships of Operations
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Understands that the product of a negative number and a positive number is negative •  Understands that multiplying whole numbers and fractions involves multiplying the whole number and the numerator, then dividing by the denominator •  Understands the additive inverse property •  Locates the additive inverse of a number on a number line •  Understands the effect of multiplying whole numbers by fractions less than 1 •  Understands that dividing by a fraction is the same as multiplying by its reciprocal •  Understands that the product of a negative number and a positive number is negative •  Understands that multiplying whole numbers and fractions involves multiplying the whole number and the numerator, then dividing by the denominator •  Determines the distance between two integers on a number line •  Understands the additive inverse property •  Understands that the product of two negative numbers is positive •  Understands that the product of a negative number and a positive number is negative Rational Numbers: Computation •  Multiplies rational numbers, including combinations of positive or negative fractions, decimals, and integers •  Adds and subtracts rational numbers, including combinations of positive or negative fractions, decimals, and integers •  Multiplies rational numbers, including combinations of positive or negative fractions, decimals, and integers •  Adds and subtracts rational numbers, including combinations of positive or negative fractions, decimals, and integers •  Divides rational numbers, including combinations of positive or negative fractions, decimals, and integers •  Multiplies rational numbers, including combinations of positive or negative fractions, decimals, and integers Rational Numbers: Equivalence •  Converts between decimals and fractions with a denominator of 3 •  Converts between decimals and fractions with a denominator of 8 •  Converts between decimals and fractions with denominators of 10 or 100 •  Converts fractions to decimals using long division •  Converts fractions to decimals using long division •  Understands the relationship between the sign of a quotient and the sign of the dividend and divisor Rational Numbers: Represent/Model •  Identifies values that are a given distance from a point on a number line Rational Numbers: Solve Real­World and Mathematical Problems •  Solves real­world problems involving the addition and subtraction of integers •  Solves real­world problems involving the addition and subtraction of integers Real/Complex Numbers: Computation •  Adds and subtracts complex numbers •  Adds and subtracts complex numbers •  Adds and subtracts complex numbers •  Simplifies expressions involving the relation i² = –1 Real/Complex Numbers: Concepts/Properties
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Determines whether the decimal expansion of a fraction repeats or terminates •  Evaluates the square root of a negative rational number Whole Numbers: Concepts/Properties •  Determines common factors •  Determines common multiples •  Solves real­world problems involving the least common multiple •  Determines least common multiples •  Solves problems involving factors and multiples •  Determines common factors •  Determines common multiples •  Solves real­world problems involving the least common multiple •  Determines least common multiples •  Solves real­world problems involving common multiples •  Solves real­world problems involving the least common multiple •  Solves real­world problems involving common multiples Whole Numbers: Multiplication/Division •  Divides whole numbers with more than four digits by two­digit divisors, with a remainder Whole Numbers: Represent and Solve Word Problems •  Solves multi­step word problems involving the four operations with whole numbers •  Solves multi­step multiplication and division word problems with whole numbers •  Solves multi­step word problems involving the four operations with whole numbers Sub­goal: Extend and Use Properties 231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts Absolute Value: Concepts/Properties •  Evaluates numerical expressions involving absolute value •  Evaluates numerical expressions involving absolute value •  Orders the absolute values of rational numbers •  Interprets the absolute value of rational numbers in terms of their relative position to 0 in a given real­world situation Algebraic Expressions
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Uses properties of exponents to simplify algebraic expressions involving whole­ number exponents •  Uses properties of exponents to simplify algebraic expressions involving whole­ number exponents •  Uses properties of exponents to simplify algebraic expressions involving fractional exponents •  Uses properties of exponents to simplify algebraic expressions involving negative integer exponents, including zero •  Uses properties of exponents to simplify algebraic expressions involving whole­ number exponents Coordinate Geometry •  Plots points in all four quadrants of a coordinate plane •  Determines the distance between two points with the same first or second coordinate Decimals: Compare/Order •  Compares decimals to the thousandths, with a different number of digits after the decimal point, using symbols •  Orders decimals to the thousandths, with a different number of digits after the decimal point Exponents •  Uses properties of exponents to simplify algebraic expressions involving whole­ number exponents •  Uses properties of exponents to simplify algebraic expressions involving whole­ number exponents •  Evaluates numerical expressions of the form (n^1/k)^k for whole numbers n and k •  Uses properties of exponents to simplify algebraic expressions involving negative integer exponents, including zero •  Uses properties of exponents to simplify algebraic expressions involving whole­ number exponents •  Uses properties of exponents to simplify algebraic expressions involving fractional exponents •  Converts between exponential and radical form •  Evaluates numerical expressions of the form (n^1/k)^k for whole numbers n and k Fractions: Equivalence •  Understands that fractions that occupy the same position on a number line are equivalent •  Writes equivalent fractions for given points on a number line Fractions: Represent/Model
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Understands fractions as the division of the numerator by the denominator •  Locates improper fractions on a number line •  Locates mixed numbers on a number line •  Understands fractions as the division of the numerator by the denominator •  Locates mixed numbers on a number line Numerical Expressions •  Uses properties of radicals to simplify radical expressions •  Evaluates numerical expressions of the form (n^1/k)^k for whole numbers n and k •  Simplifies numerical expressions involving sums and differences of radicals •  Uses properties of radicals to simplify radical expressions •  Evaluates numerical expressions of the form (n^1/k)^k for whole numbers n and k Radicals •  Uses properties of radicals to simplify radical expressions •  Converts between exponential and radical form •  Simplifies numerical expressions involving sums and differences of radicals •  Uses properties of radicals to simplify radical expressions Rational Numbers: Compare/Order •  Compares integers that represent quantities in a real­world context •  Compares integers given the meaning of zero within a real­world situation •  Orders positive rational numbers that represent quantities in a real­world context •  Writes or interprets verbal comparative statements for rational numbers within a real­world context •  Orders positive and negative rational numbers •  Orders negative rational numbers represented in multiple forms •  Orders the absolute values of rational numbers •  Orders positive and negative rational numbers •  Orders positive and negative rational numbers Rational Numbers: Equivalence •  Represents a decimal as the sum of fractions with denominators of 10 and 100 •  Converts repeating decimals to fractions Rational Numbers: Represent/Model •  Locates the opposite of a negative rational number on a number line •  Locates negative rational numbers on a number line Real/Complex Numbers: Concepts/Properties
Goal: Geometry 231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Determines whether a real number is rational or irrational •  Compares and orders real numbers •  Approximates the value of an irrational number •  Approximates the location of irrational numbers on a number line •  Determines whether a real number is rational or irrational •  Compares and orders real numbers •  Approximates the value of an irrational number •  Approximates the location of irrational numbers on a number line •  Proves statements about the sums and products of rational and irrational numbers •  Compares and orders real numbers •  Approximates the value of an irrational number •  Identifies products and sums of rational and irrational numbers as rational or irrational •  Approximates the location of irrational numbers on a number line •  Proves statements about the sums and products of rational and irrational numbers Sub­goal: Geometric Measurement and Relationships 231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts Angle Measurement •  Knows the definition of an angle •  Measures non­right angles using a protractor Area
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Determines the area of circles, given the formula •  Determines the area of rectangles given the perimeter •  Solves problems involving areas of figures composed of polygons within a real­ world or mathematical context •  Determines the area of figures composed of rectangles •  Describes the effect on area when dimensions of a rectangle are changed •  Determines the area of figures composed of polygons •  Recognizes situations which describe area •  Determines the area of triangles, formula not provided •  Determines the area of parallelograms, formula not provided •  Describes the effect on area when dimensions of a triangle are changed •  Determines the ratio between areas of scaled figures •  Determines the perimeter of rectangles given the area •  Solves problems involving both area and perimeter of rectangles within a real­world or mathematical context •  Identifies the formula for the area of a circle •  Solves problems involving areas of rectangles within a real­world or mathematical context •  Determines the area of rectangles with fractional sides, formula not provided •  Determines the circumference given the area of a circle •  Determines the radius or diameter given the area of a circle •  Determines the area of rectangles given the perimeter •  Determines the area of circles, formula not provided •  Represents the area of figures composed of rectangles using expressions or equations •  Solves problems involving areas of figures composed of polygons within a real­world or mathematical context •  Determines the area of figures composed of rectangles •  Describes the effect on area when dimensions of a rectangle are changed •  Determines the area of figures composed of polygons •  Recognizes situations which describe area •  Determines the area of triangles, formula not provided •  Determines the area of parallelograms, formula not provided •  Determines the area of trapezoids, formula not provided •  Describes the effect on area when dimensions of a triangle are changed •  Determines the ratio between areas of scaled figures •  Determines the perimeter of rectangles given the area •  Solves problems involving both area and perimeter of rectangles within a real­world or mathematical context •  Solves problems involving areas of polygons and circles, quarter circles, semicircles, or three­quarter circles within a real­world or mathematical context •  Determines the area of rectangles with fractional sides, formula not provided •  Solves area word problems involving whole numbers and tiling rectangles with non­unit squares •  Determines the area of quarter circles, semicircles, or three­quarter circles •  Determines the circumference given the area of a circle •  Determines the area of circles, formula not provided •  Describes the effect on area when the perimeter of a rectangle is changed •  Solves problems involving areas of figures composed of polygons within a real­ world or mathematical context •  Describes the effect on area when dimensions of a rectangle are changed •  Determines the area of figures composed of polygons •  Recognizes situations which describe area •  Determines the area of triangles, formula not provided •  Determines the area of trapezoids, formula not provided •  Describes the effect on area when dimensions of a triangle are changed •  Determines the ratio between areas of scaled figures •  Describes the effect on area when the radius or diameter of a circle is changed •  Determines the perimeter of rectangles given the area •  Determines the area of figures composed of polygons and circles •  Solves problems involving areas of polygons and circles, quarter circles, semicircles, or three­quarter circles within a real­world or mathematical context •  Determines the height, given the area and the sum of the bases of a trapezoid •  Solves area word problems involving whole numbers and tiling rectangles with non­unit squares •  Determines the area of quarter circles, semicircles, or three­quarter circles Circles
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Writes the equation of a circle given the center and radius •  Writes the equation of a circle given the center and radius •  Uses properties of central and inscribed angles to solve problems involving circles •  Solves problems involving inscribed angles on a diameter •  Calculates the area of sectors given the measure of the central angle •  Uses properties of chords to solve problems involving circles •  Writes the equation of a circle given the center and radius •  Uses properties of central and inscribed angles to solve problems involving circles •  Solves problems involving inscribed angles on a diameter Conic Sections •  Writes the equation of a circle given the center and radius •  Writes the equation of a circle given the center and radius •  Writes the equation of a circle given the center and radius Coordinate Geometry •  Determines the coordinates of missing vertices of geometric figures in the first quadrant given the coordinates of the other vertices •  Identifies the type of quadrilateral given the coordinates of the vertices •  Determines the coordinates of one endpoint of a line segment given the coordinates of the midpoint and the other endpoint •  Determines a side length of a polygon given the coordinates of the vertices with the same first or second coordinate •  Determines the coordinates of the midpoint of a line segment •  Determines the coordinates of one endpoint of a line segment given the coordinates of the midpoint and the other endpoint •  Determines the area of a triangle given the coordinates of the vertices •  Determines the perimeter or area of a rectangle given vertices with the same first or second coordinate •  Determines the coordinates of the midpoint of a line segment •  Writes the equation of a line parallel to a line that passes through a given point •  Writes the equation of a line parallel to a given line •  Determines the coordinates of one endpoint of a line segment given the coordinates of the midpoint and the other endpoint •  Writes the equation of a line perpendicular to a line that passes through a given point •  Determines the slope of a line perpendicular to a given line •  Determines the area of a triangle given vertices with the same first or second coordinate •  Determines the coordinates of the midpoint of a line segment •  Uses slopes to identify perpendicular lines Identification and Classification of 2­D Shapes •  Identifies and names special triangles, such as acute, right, scalene, etc., given pictures  •  Identifies properties of a 2­D shape, such as right angles, parallel sides, etc., given pictures •  Knows definitions of special triangles, such as acute, right, scalene, etc. •  Identifies properties of a 2­D shape, such as right angles, parallel sides, etc., given pictures Perimeter/Circumference
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Solves problems involving both area and perimeter of rectangles within a real­world or mathematical context •  Determines the radius or diameter given the circumference of a circle •  Determines the area of rectangles given the perimeter •  Determines the perimeter of basic polygons in which not all sides are labeled •  Determines the circumference of circles, formula not provided •  Solves problems involving perimeters of rectangles within a real­world or mathematical context •  Determines the circumference of circles, given the formula •  Determines the perimeter of rectangles given the area •  Determines the perimeter of complex figures in which not all sides are labeled •  Solves problems involving both area and perimeter of rectangles within a real­world or mathematical context •  Solves problems involving perimeters of non­rectangular polygons within a real­world or mathematical context •  Determines the radius or diameter given the circumference of a circle •  Determines the area of rectangles given the perimeter •  Determines the circumference of circles, formula not provided •  Determines the circumference given the area of a circle •  Solves problems involving perimeters of rectangles within a real­world or mathematical context •  Determines the perimeter of rectangles given the area •  Describes the effect on area when the perimeter of a rectangle is changed •  Determines the circumference of circles, formula not provided •  Determines the circumference given the area of a circle •  Determines the perimeter of rectangles given the area Points, Lines, Segments, Rays, and Angles •  Identifies perpendicular lines involving real­world objects •  Identifies perpendicular lines •  Knows the definition of an angle Problem Solving with Units •  Solves problems involving volumes of rectangular prisms within a real­world or mathematical context •  Solves problems involving both area and perimeter of rectangles within a real­world or mathematical context •  Solves problems involving areas of rectangles within a real­world or mathematical context •  Solves problems involving areas of figures composed of polygons within a real­ world or mathematical context •  Uses the net of a prism to solve surface area problems within a real­world or mathematical context •  Solves problems involving perimeters of rectangles within a real­world or mathematical context •  Solves problems involving areas of polygons and circles, quarter circles, semicircles, or three­quarter circles within a real­world or mathematical context •  Solves problems involving volumes of rectangular prisms within a real­world or mathematical context •  Solves problems involving both area and perimeter of rectangles within a real­world or mathematical context •  Solves problems involving areas of figures composed of polygons within a real­world or mathematical context •  Solves area word problems involving whole numbers and tiling rectangles with non­unit squares •  Uses the net of a prism to solve surface area problems within a real­world or mathematical context •  Solves problems involving perimeters of rectangles within a real­world or mathematical context •  Solves problems involving perimeters of non­rectangular polygons within a real­world or mathematical context •  Solves problems involving volumes of cylinders within a real­world or mathematical context •  Solves problems involving areas of polygons and circles, quarter circles, semicircles, or three­quarter circles within a real­world or mathematical context •  Solves problems involving volumes of rectangular prisms within a real­world or mathematical context •  Solves problems involving areas of figures composed of polygons within a real­ world or mathematical context •  Solves problems involving surface areas of prisms within a real­world or mathematical context •  Solves area word problems involving whole numbers and tiling rectangles with non­unit squares
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts Rates/Ratios/Proportions/Percents •  Applies the concept of density to solve problems involving area and volume •  Applies scale factors to solve problems involving scale drawings of geometric figures •  Determines scale factors in problems involving scale drawings of geometric figures •  Applies scale factors to solve problems involving scale drawings, maps, and models •  Applies the concept of density to solve problems involving area and volume •  Applies scale factors to solve problems involving scale drawings of geometric figures •  Applies scale factors to solve problems involving scale drawings, maps, and models •  Applies scale factors to solve problems involving scale drawings of geometric figures •  Applies scale factors to solve problems involving scale drawings, maps, and models Relationships involving Lines, Angles, and Polygons •  Calculates unknown angle measures using the properties of complementary, supplementary, and vertical angles •  Solves multi­step problems by applying the properties of supplementary, complementary, and vertical angles •  Calculates unknown angle measures using the properties of complementary, supplementary, and vertical angles •  Applies the Triangle Inequality Theorem •  Calculates unknown angle measures using the properties of complementary, supplementary, and vertical angles •  Applies the Triangle Inequality Theorem Similarity •  Determines scale factors in problems involving scale drawings of geometric figures •  Applies scale factors to solve problems involving scale drawings of geometric figures •  Applies scale factors to solve problems involving scale drawings, maps, and models •  Applies scale factors to solve problems involving scale drawings of geometric figures •  Applies scale factors to solve problems involving scale drawings, maps, and models •  Applies scale factors to solve problems involving scale drawings of geometric figures •  Applies scale factors to solve problems involving scale drawings, maps, and models Spatial Concepts and Symmetry •  Identifies and creates nets for pyramids •  Identifies 3­D shapes using cross­sections •  Identifies the cross­sections of 3­D shapes •  Identifies 3­D shapes using cross­ sections •  Identifies the cross­sections of 3­D shapes •  Identifies the 3­D shape created when a 2­D shape is rotated around an axis Surface Area
231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts •  Determines the surface area of rectangular prisms or cubes, formula not provided •  Uses the net of a prism to solve surface area problems within a real­world or mathematical context •  Determines the surface area of rectangular prisms or cubes, formula not provided •  Uses the net of a prism to solve surface area problems within a real­world or mathematical context •  Determines the surface area of a prism given a net •  Solves problems involving surface areas of prisms within a real­world or mathematical context •  Determines the surface area of rectangular prisms or cubes, formula not provided •  Determines the surface area of triangular prisms, formula not provided •  Determines the side length of a cube given the surface area Volume •  Determines the volume of pyramids, given the formula •  Represents the volume of rectangular prisms composed of unit cubes, using repeated addition expressions or equations •  Determines the volume of cylinders, given the formula •  Identifies units for measuring volume •  Identifies a unit cube as a unit for measuring volume •  Recognizes situations which describe volume •  Determines the volume of a rectangular prism given a net shown on a grid •  Determines the volume of figures composed of rectangular prisms •  Solves problems involving volumes of rectangular prisms within a real­world or mathematical context •  Describes the effect on volume when dimensions of a rectangular prism are changed •  Determines the length, width, or height given the volume of a rectangular prism and two of the dimensions •  Determines the volume of rectangular prisms, formula not provided •  Determines the volume of cylinders, formula not provided •  Determines the side length of a cube given the volume •  Determines the volume of pyramids, given the formula •  Represents the volume of rectangular prisms composed of unit cubes, using repeated addition expressions or equations •  Identifies units for measuring volume •  Recognizes situations which describe volume •  Describes the effect on volume when dimensions of a cylinder are changed •  Determines the volume of figures composed of rectangular prisms •  Solves problems involving volumes of rectangular prisms within a real­world or mathematical context •  Determines the volume of spheres, given the formula •  Describes the effect on volume when dimensions of a rectangular prism are changed •  Determines the volume of rectangular prisms, formula not provided •  Determines the volume of cylinders, formula not provided •  Determines the volume of pyramids, formula not provided •  Determines the volume of pyramids, given the formula •  Determines the height of a cylinder given the volume and the radius or diameter •  Solves problems involving volumes of cylinders within a real­world or mathematical context •  Describes the effect on volume when dimensions of a cylinder are changed •  Determines the volume of figures composed of rectangular prisms •  Solves problems involving volumes of rectangular prisms within a real­world or mathematical context •  Uses geometric modeling as a method to solve real­world problems with given physical or cost requirements •  Determines the radius or diameter of a cylinder given the volume and height •  Describes the effect on volume when dimensions of a rectangular prism are changed •  Represents the volume of figures composed of rectangular prisms using multiplication expressions or equations •  Determines the radius or diameter of a sphere given the volume Sub­goal: Congruence, Similarity, Right Triangles, & Trig 231­240 241­250 251­260 Reinforce these skills & concepts Develop these skills & concepts Introduce these skills & concepts Congruence
Math 6+ winter description
Math 6+ winter description
Math 6+ winter description
Math 6+ winter description
Math 6+ winter description
Math 6+ winter description
Math 6+ winter description

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